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3.9: Useful techniques – demand and supply equations

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    45741
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    The supply and demand functions, or equations, underlying Table 3.1 and Figure 3.2 can be written in their mathematical form:

    img56.png img57.png

    A straight line is represented completely by the intercept and slope. In particular, if the variable P is on the vertical axis and Q on the horizontal axis, the straight-line equation relating P and Q is defined by P=a+bQ. Where the line is negatively sloped, as in the demand equation, the parameter b must take a negative value. By observing either the data in Table 3.1 or Figure 3.2 it is clear that the vertical intercept, a, takes a value of $10. The vertical intercept corresponds to a zero-value for the Q variable. Next we can see from Figure 3.2 that the slope (given by the rise over the run) is 10/10 and hence has a value of –1. Accordingly the demand equation takes the form P=10–Q.

    On the supply side the price-axis intercept, from either the figure or the table, is clearly 1. The slope is one half, because a two-unit change in quantity is associated with a one-unit change in price. This is a positive relationship obviously so the supply curve can be written as P=1+(1/2)Q.

    Where the supply and demand curves intersect is the market equilibrium; that is, the price-quantity combination is the same for both supply and demand where the supply curve takes on the same values as the demand curve. This unique price-quantity combination is obtained by equating the two curves: If Demand=Supply, then

    10–Q=1+(1/2)Q.

    Gathering the terms involving Q to one side and the numerical terms to the other side of the equation results in 9=1.5Q. This implies that the equilibrium quantity must be 6 units. And this quantity must trade at a price of $4. That is, when the price is $4 both the quantity demanded and the quantity supplied take a value of 6 units.

    Modelling market interventions using equations

    To illustrate the impact of market interventions examined in Section 3.7 on our numerical market model for natural gas, suppose that the government imposes a minimum price of $6 – above the equilibrium price obviously. We can easily determine the quantity supplied and demanded at such a price. Given the supply equation

    P=1+(1/2)Q,

    it follows that at P=6 the quantity supplied is 10. This follows by solving the relationship 6=1+(1/2)Q for the value of Q. Accordingly, suppliers would like to supply 10 units at this price.

    Correspondingly on the demand side, given the demand curve

    P=10–Q,

    with a price given by img58.png, it must be the case that Q=4. So buyers would like to buy 4 units at that price: There is excess supply. But we know that the short side of the market will win out, and so the actual amount traded at this restricted price will be 4 units.


    This page titled 3.9: Useful techniques – demand and supply equations is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by Douglas Curtis and Ian Irvine (Lyryx) .

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